Algorithms for Stable Roommate with Externalities

TL;DR

This paper explores stable roommate assignments with externalities, proposing algorithms for 4-person stability that are Pareto optimal and strategy-proof, and analyzing the complexity of finding 2-person stable assignments under various conditions.

Contribution

It introduces a serial dictatorship algorithm for 4PS stability that is Pareto optimal and strategy-proof, and identifies preference structures allowing polynomial-time solutions for 2PS stability.

Findings

Serial dictatorship algorithm achieves 4PS Pareto optimality and strategy-proofness.

Variations of top trading cycle algorithms are not strategy-proof or Pareto optimal.

Certain preference structures enable polynomial-time 2PS assignment determination.

Abstract

In the roommate matching model, given a set of 2n agents and n rooms, we find an assignment of a pair of agents to a room. Although the roommate matching problem is well studied, the study of the model when agents have preference over both rooms and roommates was recently initiated by Chan et al. [11]. We study two types of stable roommate assignments, namely, 4-person stable (4PS) and 2-person stable (2PS) in conjunction with efficiency and strategy-proofness. We design a simple serial dictatorship based algorithm for finding a 4PS assignment that is Pareto optimal and strategy-proof. However, the serial dictatorship algorithm is far from being 2PS. Next, we study top trading cycle (TTC) based algorithms. We show that variations of TTC cannot be strategy-proof or PO. Finally, as Chan et al. (2016) showed that deciding the existence of 2PS assignment is NP-complete, we identify preference structures where a 2PS assignment can be found in polynomial time.